We present a detailed investigation of the magnetic and superconducting properties of Ca1-xNaxFe2As2 single crystals with x=0.00, 0.35, 0.50, and 0.67 by means of the local probe techniques Mössbauer spectroscopy and muon spin relaxation experiments. With increasing Na-substitution level, the magnetic order parameter is suppressed. For x=0.50 we find a microscopic coexistence of magnetic and superconducting phases accompanied by a reduction of the magnetic order parameter below the superconducting transition temperature Tc. A systematic comparison with other 122 pnictides reveals a square-root correlation between the reduction of the magnetic order parameter and the ratio of the transition temperatures Tc/TN, which can be understood in the framework of a Landau theory. In the optimally doped sample with Tc≈34 K, diluted magnetism is found and the temperature dependence of the penetration depth and superfluid density are obtained, proving the presence of two superconducting s-wave gaps. © 2015 American Physical Society.